Question

Calculate the molar volume occupied by 1 mole of N2 using the van der Waals equation in the form of virial expansion at (a) its critical temperature and (b) its Boyle temperature. Assume that the pressure is 10 atm throughout. At what temperature is the gas most perfect? Use the following data: Tc = 126.3 K, a=1.352 L2 atm mol-2, b = 0.0387 L mol-1

Answer 1

Answer:

Explanation:

Given that:

Pressure P = 10 atm

number of moles of N$_2$ = 1 mole

correction for the attractive force between molecule a = 1.352

correction for the volume of molecules  b = 0.0387 L mol-1

Rate = 8.314

critical Temperature Tc= 126.3 K

Using van deer Waal equation:

$(p+ \dfrac{n^2a}{V^2} ) (V-nb)=nRT$

So for 1 mole of N$_2$ gas; we have

$(p+ \dfrac{a}{V^2} ) (V-b)=RT$

$(10+ \dfrac{1.352}{V^2} ) (V-0.0387)=8.314 \times 126.3$

Recall that: Tc = $\dfrac{ 8a}{27Rb}$

and

$Pc=\dfrac{a}{27b^2}$

Vc = 3b

Thus;

Vc= 3×(0.0387)

Vc  = 0.1161m³

using the above Van der Waal equation, the value of V can also be determined, but in several situations, we abandon the term of (V - nb) and sometimes abandon $(p+n^2*\dfrac{a}{V^2})$ depending on the circumstances.